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3 years ago

Identify the mean of each distribution.

Mathematics

2 answers:

Setler [38]3 years ago

6 0

Answer:

Distribution A : 50

Distribution B : 100

Distribution C : 200

Second part is : B,C,A

Step-by-step explanation:

Alex787 [66]3 years ago

5 0

Answer:

50, 100, 200 and part 2 is b,c,a

Step-by-step explanation:

e2020

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For two events A and B show that P (A∩B) ≥ P (A)+P (B)−1.

nordsb [41]

Answer:

<h3>For two events A and B show that P (A∩B) ≥ P (A)+P (B)−1.</h3>

By De morgan's law

$(A\cap B)^{c}=A^{c}\cup B^{c}\\\\P((A\cap B)^{c})=P(A^{c}\cup B^{c})\leq P(A^{c})+P(B^{c}) \\\\1-P(A\cap B)\leq P(A^{c})+P(B^{c}) \\\\1-P(A\cap B)\leq 1-P(A)+1-P(B)\\\\-P(A\cap B)\leq 1-P(A)-P(B)\\\\P(A\cap B)\geq P(A)+P(B)-1$

which is Bonferroni’s inequality

<h3>Result 1: P (Ac) = 1 − P(A)</h3>

Proof

If S is universal set then

$A\cup A^{c}=S\\\\P(A\cup A^{c})=P(S)\\\\P(A)+P(A^{c})=1\\\\P(A^{c})=1-P(A)$

<h3>Result 2 : For any two events A and B, P (A∪B) = P (A)+P (B)−P (A∩B) and P(A) ≥ P(B)</h3>

Proof:

If S is a universal set then:

$A\cup(B\cap A^{c})=(A\cup B) \cap (A\cup A^{c})\\=(A\cup B) \cap S\\A\cup(B\cap A^{c})=(A\cup B)$

Which show A∪B can be expressed as union of two disjoint sets.

If A and (B∩Ac) are two disjoint sets then

$P(A\cup B) =P(A) + P(B\cap A^{c})---(1)\\$

B can be expressed as:

$B=B\cap(A\cup A^{c})\\$

If B is intersection of two disjoint sets then

$P(B)=P(B\cap(A)+P(B\cup A^{c})\\P(B\cup A^{c}=P(B)-P(B\cap A)$

Then (1) becomes

$P(A\cup B) =P(A) +P(B)-P(A\cap B)\\$

<h3>Result 3: For any two events A and B, P(A) = P(A ∩ B) + P (A ∩ Bc)</h3>

Proof:

If A and B are two disjoint sets then

$A=A\cap(B\cup B^{c})\\A=(A\cap B) \cup (A\cap B^{c})\\P(A)=P(A\cap B) + P(A\cap B^{c})\\$

<h3>Result 4: If B ⊂ A, then A∩B = B. Therefore P (A)−P (B) = P (A ∩ Bc) </h3>

Proof:

If B is subset of A then all elements of B lie in A so A ∩ B =B

$A =(A \cap B)\cup (A\cap B^{c}) = B \cup ( A\cap B^{c})$

where A and A ∩ Bc are disjoint.

$P(A)=P(B\cup ( A\cap B^{c}))\\\\P(A)=P(B)+P( A\cap B^{c})$

From axiom P(E)≥0

$P( A\cap B^{c})\geq 0\\\\P(A)-P(B)=P( A\cap B^{c})\\P(A)=P(B)+P(A\cap B^{c})\geq P(B)$

Therefore,

P(A)≥P(B)

8 0

3 years ago

A wheel has a diameter of cm.How many revolutions does it make to cover 154m?

SCORPION-xisa [38]

Answer:

154<em>divided</em><em> </em><em>by</em><em> </em><em>tounsend</em>

Step-by-step explanation:

second convert 154into mettres

8 0

2 years ago

An item has a listed price of $65 . If the sales tax rate is 3%, how much is the sales tax (in dollars)?

larisa86 [58]

Answer:

$1.95 hope this helped

Step-by-step explanation:

3 0

3 years ago

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Justin is training for a hamburger eating competition. He is eventually able to eat 15 hamburgers in 10 minutes. What is justin’

user100 [1]

Answer:

1.5 hamburgers per minute

Step-by-step explanation:

In 10 minutes, Justin can eat 15 burgers.

In 1 minute, Justin can eat 15/10 burgers.

15/10 = 1.5

7 0

3 years ago

What is the difference between 120 yards and 110 meters in feet

natita [175]

The answer is 27.2. (meter is bigger)
1 yard = 91.44 centimeters, and 1 meter= 100 centimeters

91.44 * 120 = 10972.8

100*110 = 11000

3 0

3 years ago

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